The present invention relates to noise reduction processing in the field of image processing and in particular to a filter for reducing noise without causing image blurring or density unevenness.
Since noise reduction processing basically functions to smooth a rapid change of density, it has an effect of blurring outlines of figures. Therefore, there is noise reduction processing called edge preserving smoothing, in which outlines of figures are roughly estimated by using some method, and smoothing is conducted so as not to hamper them. Representative papers describing such noise reduction processing are as follows:
(1) H. Harashima, K. Odajima, Y. Shishikui and H. Miyakawa, ".epsilon.-Separaing Nonlinear Digital Filter and Its Applications", The Trans. of The Institute of Electronics and Communication Engineers of Japan [A]), Vol. J65-A, No. 4, pp. 297-304 (April 1982);
(2) P. Perona and J. Malik, "Scale-Space and Edge Detection Using Anisotoropic Diffusion", IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 12, No. 7, July 1990, pp. 629-639; and
(3) J-S. Lee, "Digital Image Enhancement and Noise Filtering by Use of Local Satistics", IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. PAMI-2, No. 2, March 1980, pp. 165-168.
According to methods described in these papers, a degree of edge structure is defined in a local region according to the differential value or local variance value, and the effect of smoothing is adjusted according to the degree of its edge structure. A local structure is recognized on the basis of whether it is an edge, and its directionality is not considered. This results in a problem that enhancing the noise reducing effect with respect to an image having a poor signal-to-noise ratio tends to cause blurring in edges or density unevenness.
Furthermore, in JP-A-4-188283, a technique for detecting edges of binary images, smoothing edges, and reconstructing multi-valued images is described. In this technique, the direction of the edge is detected, and out of a plurality of smoothing filters used for smoothing regions differing in shape of spatial region and distribution of coefficient, one filter is selected according to the direction of the edge to reduce blurring of figures on images.
On the other hand, as an exemplary the method for performing smoothing by taking the local structure of the image into consideration, there is a method using local template matching. This method is described in "Digital Image Processing For Understanding Image [I]", written by Junichiro Toriwaki and published by Shokodo on Nov. 30, 1989, pp. 112-114. This method includes preparing typical patterns of density curved surfaces in local regions of images in the form of templates, making a match between an input density value at U((i, j)) in a neighborhood of each pixel (i, j) of the image and a template so as to select a template suited to the local structure of the neighborhood U((i, j)), and conducting smoothing processing. Specifically, first of all, some samples of partial image (templates) are prepared beforehand. On the other hand, arrangement of input density values at U((i, j)) in the neighborhood of the pixel (i, j) in a predetermined order is regarded as a One-dimensional vector and represented as F.sub.ij. Templates are also arranged in a similar order to form a one-dimensional vector and represented as A.sub.1, A.sub.2, . . . , A.sub.m. At this time, with respect to a function S representing the degree of conformity of each template in (i, j), EQU k.sub.0 =min S (F.sub.ij, A.sub.k)
is calculated. By using a template Ak0 as a weighting function, smoothing processing is conducted on the basis of pixel values included in U((i, j)) of the pixel (i, j). As for the concrete form of the function S representing the degree of conformity, a wide variety of forms have been contrived in the field of numerical classification in pattern recognition and statistics.